Research on Morlet Wavelet Based Lamb Wave Spatial Sampling Signal Optimization Method

In recent years, Lamb wave and piezoelectric transducers (PZTs) array based wavenumber filtering technique for damage estimation has been gradually studied. Compared with the time domain and frequency domain analysis of the Lamb wave signals, the wavenumber domain analysis is an effective approach to distinguish wave propagating direction and wave modes. However, the spatial resolution sampled by the PZTs is lower than that sampled by scanning laser Doppler vibrometer. As for the diameter of the PZT, it cannot be very small. In this paper, a new Lamb wave spatial sampling signal optimization method based on Morlet wavelet is proposed. Firstly, the frequency band parameter of the Morlet mother wavelet function is calculated by the Lamb wave excitation signal. Then, the sum of squared errors between the Lamb wave spatial sampling signal and the Morlet wavelet function fitting waveform at each scale factor and time factor is calculated. Finally, the scale factor and time factor corresponding to the least sum of squared errors can be judged to be the best match scale factor and time factor respectively, and the Morlet wavelet function fitting waveform in that scale factor and time factor can be seen as the optimized Lamb wave spatial sampling signal. The validation experiment performed on a glass fiber epoxy composite plate shows that the proposed method can improve the spatial resolution and length of the Lamb wave spatial sampling signal, and the sum of squared errors of this method is no more than 0.2.